Question

The difference between the simple interest and compound interest on a certain sum is rupees 54.40 for 2 years at 8% per annum. Find the sum in rupees.

Answer 1

Question:

The difference between the simple interest and compound interest on a certain sum is rupees 54.40 for 2 years at 8% per annum. Find the sum in rupees.

Step-by-step explanation:

p = 500

➡ Given :

• Difference between Simple intereat and compund interest = 54.4

• Time Elapsed = 2 years.

• Rate of interest = 8%

➡ To Find :

• Sum in rupees.

➡ Procedure :

$\boxed{\sf \: SI = \dfrac{p \times r \times t}{100} }$

$\sf \: \implies \: \dfrac{p \times 8 \times 2}{100}$

$\sf \implies \: \dfrac{4 \: p}{25}$

$\sf \implies \: \dfrac{4 \: p}{100}$

$\boxed{\sf \: amount = p \bigg(1 + \frac{r}{100} \bigg) ^{n} }$

$\sf \implies \: p \bigg(1 + \frac{2}{25} { \bigg)}^{2}$

$\sf \: \implies \: p \bigg( {\dfrac{27}{25} \bigg) }^{2}$

$\implies \:a = \frac{729p}{625}$

☆ Compund interest = Amount - Principal

$\implies \: \: CI = \frac{729p}{625} - p$

$\sf \implies \: 54.40 = \frac{729p}{625} - p - \frac{4p}{25}$

$\implies \: 54.40 = p( \frac{729 - 625 - 100)}{625} )$

$\implies \: 625 \times 54.40 = p(729 - 625 - 100)$

$\implies \: 625 \times 5.40 = 4p$

${ \huge \boxed{{\bold{ans = p = 500}}}}$